Evaluation of deflection amplification factor in steel moment‐resisting frames

Steel moment‐resisting frames (SMRFs) are the most common type of structural systems used in steel structures. The first step of structural design for SMRFs starts with the selection of the structural sections on the basis of story drift limitation. ASCE 7 (2010) requires that the inelastic story drifts be obtained by multiplying the deflections determined by elastic analysis under design earthquake forces with a deflection amplification factor (C_d). For special moment‐resisting frames, C_d is given as 5.5 in ASCE 7 (2010). Lower C_d values will increase the overall inelastic response of the structure. On the other hand, the inelastic response of the structure is expected to be less severe when designed for higher C_d values. The performance objective is that the structure should sustain the inelastic deformation demand imposed due to design earthquake ground motions. This study aims at investigating the inelastic seismic response that low‐rise, medium‐rise and high‐rise SMRFs can experience under design earthquake ground motions and maximum considered earthquake (MCE) level ground motions and evaluating the deflection amplification factors (C_d) for SMRFs in a rational way. For this purpose, nonlinear dynamic time history and pushover analyses will be carried out on SMRFs with 4, 9 and 20 stories. The results indicate that the current practice for computing the inelastic story drifts for SMRFs is rational and the frames designed complying with the current code requirements can sustain the inelastic deformations imposed during design earthquake ground motions when seismically designed and detailed. Copyright © 2013 John Wiley & Sons, Ltd.     

Reliable fragility functions for seismic collapse assessment of reinforced concrete special moment resisting frame structures under near‐fault ground motions

A collapse fragility function shows how the probability of collapse of a structure increases with increasing ground motion intensity measure (IM). To have a more reliable fragility function, an IM should be applied that is efficient and sufficient with respect to ground motion parameters such as magnitude (M) and source‐to‐site distance (R). Typically, pulse‐like near‐fault ground motions are known by the presence of a velocity pulse, and the period of this pulse (T_p) affects the structural response. The present study investigates the application of different scalar and vector‐valued IMs to obtain reliable seismic collapse fragility functions for reinforced concrete special moment resisting frames (RC SMRFs) under near‐fault ground motions. The efficiency and sufficiency of the IMs as the desirable features of an optimal IM are investigated, and it is shown that seismic collapse assessments by using most of the IMs are biased with respect to T_p. The results show that (Sa(T₁), Sa(T₁)/DSI) has high efficiency and sufficiency with respect to M, R, T_p, and scale factor for collapse capacity prediction of RC SMRFs. Moreover, the multiobjective particle swarm optimization algorithm is applied to improve the efficiency and sufficiency of some advanced scalar IMs, and an optimal scalar IM is proposed.     

Estimation of seismic demands of steel frames subjected to near‐fault earthquakes having forward directivity and comparing with pushover analysis results

High statistics of damages in modern structures (buildings structured based on new codes) exposed to near‐fault earthquake illustrates the necessity of more studies on this kind of earthquake effects on the structures. A specification of near‐fault earthquakes is the directivity effects. Existing records of near‐fault quakes containing directivity effects including records of Iran and abroad were modified and used for linear time history analysis of three steel moment frames (5, 8 and 12 story frames), and the results were compared with nonlinear time history analysis and pushover analysis of far‐fault quakes in this paper. The results showed that these records (near fault) motivate high modes of the structure, and especially for the 12‐story structure, high response was detected, but none of these results made the frames collapse. By comparing nonlinear dynamic analysis (time history) with nonlinear static analysis (pushover), it was concluded that various lateral load patterns in pushover cannot cover the time history result needs. Load distribution pattern based on the first vibration mode covers these demands in the lower floors, but in higher floors, this method is not applicable. Copyright © 2012 John Wiley & Sons, Ltd.     

Structural response of vertically irregular tall moment‐resisting steel frames under pre‐ and post‐earthquake fire

Post‐earthquake fires (PEF) may result in a catastrophe in urban regions even worse than the earthquake itself. Most urban structures are not designed to resist two subsequent extreme loads such as earthquake and fire. Thus, these types of structures are too weak when subjected to the PEF loads. On the other hand, it is well understood that irregular building structures are more susceptible to sustain earthquake damage than regular buildings. Investigating irregular buildings can therefore be more important when there is a high possibility of PEF. While there are various irregularities, here, vertical irregularity is considered. The study is performed on one irregular seven‐story tall moment‐resisting steel frame designed based on the American Society of Civil Engineers code. The frame is firstly subjected to an earthquake load with the peak ground acceleration of 0.35 g and then is exposed to a generalized exponential fire curve. To make a comparison between the results, the PEF analysis is also performed for the regular frame. The results show that there is a marked difference between the PEF of the regular frame with that of the irregular frame. In addition, two types of failure—local and global—were observed during the analysis, where the local collapse is related to the deflection of beams, and the global collapse is pertained to the considerable movement of the columns. It is observed during the analysis that the irregular frames are more susceptible to collapse globally. Copyright © 2015 John Wiley & Sons, Ltd.     

Dual‐steel frame consisting of moment‐resisting frame and shape memory alloy braces subjected to near‐field earthquakes

In this paper, concentric braced frames are combined with moment‐resisting frame (MRF) as a dual system subjected to near‐field (NF) pulse‐like and far‐field ground motions. The braced frame in this system configuration consists of steel buckling‐restrained braces (BRB model), braces with shape memory alloy (SMA model), or combination of BRB and SMA braces (COMBINED model). Some prototype structures of the proposed systems are designed according to the code recommendations. Then, the nonlinear models of the considered structures are developed in SeismoStruct software, and nonlinear time history analysis (NLTHA) is implemented. NLTHA is performed subjected to earthquake record sets at maximum considered earthquake (MCE) and design base earthquake (DBE) levels, and responses of the systems are investigated and compared with each other. Among the examined models, the SMA and COMBINED models exceed the CP level subjected to NF‐MCE record set. Therefore, more investigation is needed for using short‐segment SMA braces in the dual‐steel frames in NF area.     

Performance evaluation of special and intermediate moment‐resisting reinforced concrete frames using pushover and incremental dynamic analysis

In this study, the seismic performance of special and intermediate moment‐resisting reinforced concrete frames are evaluated through nonlinear static and dynamic analysis. According to experimental studies, one of the most important parameters affecting the behavior of special and intermediate ductile reinforced concrete frames is the transverse reinforcement ratio. In this paper, constitutive law of material for concrete under the influence of various transverse reinforcement ratios have been derived using Mander et al. model, and 20 ground‐motion accelerograms have been utilized for dynamic analysis. Additionally, the results of pushover and incremental dynamic analysis were compared in order to evaluate seismic performance of the selected high‐rise structures. Results reveal that both types of reinforced concrete frames with beam‐hinge type failure mechanisms have ductile behavior. Special moment frames have higher ductility because of early entry into nonlinear range resulting in higher plastic rotations, which result in greater lateral displacements. Due to the differences in behavior of intermediate and special ductility frames, confinement has an important role in the ductile behavior of structures. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic performance of steel mega braced frames equipped with shape‐memory alloy braces under near‐fault earthquakes

This paper has two main objectives. The first objective is to compare the dynamic behavior of mega shape‐memory alloy (SMA) braced frames subjected to far‐fault and near‐fault ground motions. Therefore, four mega SMA braced frames with various stories located in the vicinity of an active fault were considered. Fourteen near‐fault records with two well‐known characteristics of these records, i.e. forward directivity and fling step, were selected to test near‐fault earthquake characteristics. Furthermore, other seven far‐field records were selected for comparison. Through the nonlinear dynamic analyses, the results showed that for high‐rise frames, the near‐fault earthquakes resulted in more demands than the far‐field, but for low‐rise frames, far‐fault records imposed more demands. It was also found that mega configuration and SMA stiffening at large strains played key roles in seismic vibration control of frames. The second objective of this paper is to study the superior performance of SMA braces over the buckling restrained braces by exploiting the super‐elastic characteristic of the SMA. Identical buildings equipped with buckling restrained braces were also studied for comparison purposes. The results revealed the excellent performance of SMA braces under near‐fault records by reducing both interstory drift and residual displacement of the top floor. Copyright © 2015 John Wiley & Sons, Ltd.     

Plastic hinge length of reinforced concrete columns subjected to both far‐fault and near‐fault ground motions having forward directivity

In a strong earthquake, a standard reinforced concrete (RC) column may develop plastic deformations in regions often termed as plastic hinge regions. A plastic hinge is basically an energy dampening device that dampens energy through the plastic rotation of a rigid column connection, which triggers redistribution of bending moments. The formation of a plastic hinge in an RC column in regions that experience inelastic actions depends on the characteristics of the earthquakes as well as the column details. Recordings from recent earthquakes have provided evidence that ground motions in the near field of a rupturing fault can contain a large energy or ‘directivity’ pulse. A directivity pulse occurs when the propagation of the fault proceeds at nearly the same rate as the shear wave velocity. This pulse is seen in the forward direction of the rupture and can cause considerable damage during an earthquake, especially to structures with natural periods that are close to those of the pulse. In the present paper, 1316 inelastic time‐history analyses have been performed to predict the nonlinear behaviour of RC columns under both far‐fault and near‐fault ground motions. The effects of axial load, height over depth ratio and amount of longitudinal reinforcement, as well as different characteristics of earthquakes, were evaluated analytically by finite element methods and the results were compared with corresponding experimental data. Based on the results, simple expressions were proposed that can be used to estimate plastic hinge length of RC columns subjected to both far‐fault and near‐fault earthquakes that contain a forward‐directivity effect. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance of steel moment‐resisting beam‐supporting column transfer structures under fire

This paper investigates the structural fire response of steel beam‐supporting column transfer structures. Two three‐story (Case 1) and seven‐story (Case 2) structures with different span lengths are designed first to withstand gravity and seismic loads. All the structural members are also designed to meet their required fire resistance ratings based on the ISO834 fire. The structural vulnerability is then evaluated under two fire scenarios: the natural fire as a uniform and the traveling fire as a nonuniform temperature distribution inside the structures. The fire loads are applied to the first story of the structures where the structural irregularity is evident. The natural fires are determined based on Eurocode 1 and based on different opening ratios of 0.04, 0.067, 0.08, 0.12, and 0.16 to provide different duration of the heating phase. The results indicate that under the uniform fire scenarios, Case 1 collapses after 134 min under the opening ratio of 0.04. As well, Case 2 collapses under the opening ratios of 0.04, 0.67, and 0.08 at 95, 142, and 160 min, respectively. The results also show that under the nonuniform fire with a size of 25%; Case 1 collapses at 89 min, and Case 2 collapses at 93 min. Although it is believed that the cases studied should logically remain stable under possible fire scenario, the results indicate that this is not a true presumption. The results of this study provide beneficial information about structural fire response of beam‐supporting column transfer structures as an important structural irregularity.     

Energy dissipation of tall core‐wall structures with multi‐plastic hinges subjected to forward directivity near‐fault and far‐fault earthquakes

In this study, different energy components in the tall reinforced concrete core‐wall buildings with numerous plastic hinges over the height are investigated using nonlinear time history analysis. The effect of near‐fault and far‐fault earthquakes is compared. The idea of one‐plastic, two‐plastic, three‐plastic and whole‐plastic hinge approaches along the core wall is examined. The input energy, inelastic, damping, kinetic and elastic strain energy during the earthquakes are studied. The results show that a large energy quantity transfers to the structure at the arrival time of the near‐fault motion pulse. Inelastic energy distribution over the height shows a considerable amount of inelastic energy dissipation occurring at the base and above the mid‐height of the walls. Copyright © 2016 John Wiley & Sons, Ltd.     

Forward directivity near‐fault and far‐fault ground motion effects on the behavior of reinforced concrete wall tall buildings with one and more plastic hinges

Near‐fault (NF) ground motion having forward directivity and far‐fault (FF) earthquakes can generate different responses on tall reinforced concrete cantilever walls. In this paper, the behavior of the core wall buildings were examined by performing nonlinear time history analyses on 20‐story, 30‐story and 40‐story fiber element models. The concept of one, two, three and extended plastic hinge in the core walls subjected to the NF motions having forward directivity (pulse‐like) and FF motion was studied by carrying out inelastic dynamic analysis. At the upper levels of the walls, NF pulse‐like ground motions can produce considerably larger curvature ductility, inter‐story drift and displacement demands as compared with the FF motions. A new approach was proposed to obtain the moment demand and reinforcement required to balance the curvature ductility demand along the height of a core wall. Copyright © 2015 John Wiley & Sons, Ltd.     

The modified dynamic‐based pushover analysis of steel moment resisting frames

A modified dynamic‐based pushover (MDP) analysis is proposed to properly consider the effects of higher modes and the nonlinear behavior of the structural systems. For this purpose, first, a dynamic‐based story force distribution (DSFD) load pattern is constructed using a linear dynamic analysis, either time history (THA) or response spectrum (RSA). Performing an initial pushover analysis with the DSFD load pattern, a nonlinearity modification factor (NMF) is calculated to modify the DSFD load pattern. The envelope of the peak responses of the structure obtained from 2 pushover analyses with the modified DSFD load pattern as well as the code suggested first mode load pattern are considered as the final demand parameters of the structural system. The efficiency of the proposed MDP procedure is investigated using the results of nonlinear THA besides some existing pushover procedures. For this purpose, the 2‐dimensional 9‐, 15‐, and 20‐story, SAC steel frame building models are considered for parametric studies using OpenSees program. The results indicate that the proposed MDP‐THA and MDP‐RSA methods can significantly improve the performance of the pushover analysis. Considering the accuracy and calculation efforts, the MDP‐RSA method is strongly suggested as an efficient and applicable method to estimate the nonlinear response demands of steel moment resisting frames.     

Seismic performance of steel braced frames with self‐centering buckling‐restrained brace utilizing superelastic shape memory alloys

Buckling‐restrained braced frame (BRB) is one of the newest seismic force‐resisting systems used in buildings. However, one of the requirements for designing a structure is to provide a ductility behavior of structures to dissipate earthquake energy and to avoid residual drifts. These days, self‐centering seismic lateral force‐resisting systems have drawn attention due to their potentials to solve the above mentioned issues. On the other hand, shape memory alloys (SMAs) are characterized by unique superelastic behavior, which enables the material to recover its original shape after experiencing large deformations. The goal of this study is to assess BRBs whose ductility are improved by utilizing SMA. Nonlinear time history and incremental dynamic analysis techniques are applied to investigate the behavior of the two frames with different stories (four and eight stories) under different ground motion records. The results showed that utilizing BRB made of hybrid steel and SMA resulted in increasing ductility of the structure and decreasing residual displacements of the structures.     

Fundamental period of irregular moment‐resisting steel frame structures

The determination of the fundamental period of vibration of a structure is essential to earthquake design. Current code equations such as American Society of Civil Engineers Standard (ASCE) 7‐10 provide formulas for the approximate period of moment‐resisting frames (MRFs), which are dependent only on the height of the structure or number of stories. Such a formulation is overly conservative and unable to account for structures with geometric irregularities. This study investigated the fundamental periods of MRFs with varying geometric irregularities. The fundamental periods based on vibration theory for each example were compared with empirical equations, including current code equations as well as equations proposed in recent literature. New equations are proposed for the fundamental periods of MRFs, which take into account vertical and horizontal irregularities. Through statistical comparison, it was found that a three‐variable power model that is able to account for irregularities resulted in a better fit to the Rayleigh data than equations that were dependent on height only. The proposed equations were validated through a comparison of available measured period data for MRFs. They will allow design engineers to quickly estimate the fundamental period of MRF structures by taking into account irregularities. Copyright © 2013 John Wiley & Sons, Ltd.     

Fundamental period of masonry infilled moment‐resisting steel frame buildings

It is known to be a necessary practice to study the effect of infill walls on fundamental period and revise the equations included in the current building codes. In this research, the fundamental period of vibration, by modeling an infill wall as a compression strut in three‐dimensional numerical models of moment‐resisting steel frames, was studied. Areas studied in the present research were structures of symmetric infill wall arrangements wherein the effects of various infill percentage, various moduli of elasticity of masonry wall materials, and different numbers of spans were investigated. The mean fundamental period obtained by the formula provided in FEMA450 was 1.3 times greater than the value resulted from the numerical modeling of infilled moment‐resisting steel frames. Moreover, the corresponding coefficient of determination, R², of the curve fitted to numerically obtained periods was found to be 0.65 when the fundamental period of the infilled frames was only estimated based on the height of buildings, indicating a great deal of variation within the results. A new formula was proposed to estimate the fundamental period based on the structure height, infill wall percentage, and modulus of elasticity, at an acceptable level of accuracy so that the R² coefficient was determined to be 0.99 for the results of the proposed formula.     

Behavior of moment‐resisting tall steel structures exposed to a vertically traveling post‐earthquake fire

An investigation is performed on a 10‐story moment‐resisting steel structure designed to the Life Safety level of performance of the Federal Emergency Management Agency (FEMA) 356 code by exposing it to post‐earthquake fire (PEF). The fire curve is accounted for using the natural fire method, and the fire is subjected to the floors vertically in three different scenarios: (a) fire initiated from the first floor, (b) fire initiated from the fourth floor and (c) fire initiated from the seventh floor. A delay of 5 minutes and 25 minutes are considered for spreading the fire between the floors. To make a comparison between the results, a concurrent fire is also considered for the fire analysis. The results indicate that the PEF resistance of the frame exposed to the concurrent fire and the 5 minutes delay is much lower than that with a delay of 25 minutes. The results also show that subjecting the frame to a delayed fire of 25 minutes leads to the collapse of the frame during cooling phase, whereas in the other scenarios, the frame collapses during heating phase. As a result, more considerations need to be implemented in the codes on top of that for the PEF itself and that is the appropriate rate of spread of fire between floors. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytical investigation on performance of special moment‐resisting connections with unequal beam depths

This study considers the effect of detailing of an interior beam to column connection with unequal beam depths on seismic performance of special moment‐resisting frame (SMRF), which has not explicitly been taken into account, despite its possible occurrence in engineering practice, by the current codes and provisions. Studied detailing consists of a continuity plate arrangement, cover plate, flange plate and haunch connection system as alternatives in order to connect a shallow beam and a deep beam to column. To improve the understanding of seismic performance in SMRF connections, coordinated analytical and experimental studies have been conducted to examine the effect of different geometries and the mentioned alternatives on the seismic performance of SMRF with unequal beam depths. This work describes the analytical studies and includes a summary of the experimental results used in the development and validation of the analytical models; the experiment and analyses show that some detailing could provide ductile behavior with a total storey drift angle of 0.06 rad before experiencing 20% strength degradation while other detailing would not satisfy this criterion. Copyright © 2015 John Wiley & Sons, Ltd.     

Influence of infill configurations on seismic responses of steel self‐centering moment resisting frames

Steel self‐centering moment resisting frames (SC‐MRFs) have been validated experimentally as resilient structural systems, mainly highlighting the minimized residual drift responses but are prone to suffering high‐mode effects. In this paper, the influence of infill configurations on seismic responses of steel SC‐MRFs was first analyzed. A comparison of the previous experimental results was conducted to investigate the effect of infills on the residual drift of steel frames. In the numerical simulation, the infills were modeled as the equivalent strut diagonals, and the force–displacement of the infills was modeled using the combination of Elastic‐No Tension Material and Hysteretic Material offered by the OpenSees program. The seismic analyses of 3‐ and 9‐story SC‐MRFs with and without infills were carried out to analyze the effects of infills on the residual drift responses and high‐mode contribution under the selected ground motions. Finally, the different infill types and infill irregularities on the seismic responses were investigated to obtain general conclusions. The plastic deformations of columns and infills are also compared in the different cases of infill configurations. The results reveal that all infilled cases experience reduced peak‐story drift and force demands at the upper stories.     

Seismic retrofit of a high‐rise steel moment‐resisting frame using fluid viscous dampers

The Tall Building Initiative project of Pacific Earthquake Engineering Research Center has been expanded to investigate the seismic performance and possible retrofit of existing tall buildings. A candidate 35‐story steel building with representative details from the early 1970s was analyzed following several guidelines, which revealed a wide range of potential inadequacies. Thus, a two‐level retrofit approach was examined that focused on achieving the collapse prevention limit state under the major basic safety earthquake (BSE‐2E) hazard level prescribed by ASCE 41. This paper focused on a Level‐2 retrofit that used fluid viscous dampers to augment Level‐1 retrofits. For this approach, feasible damper locations and overall effective damping ratios were first evaluated through a series of preliminary studies, and then a two‐phase design method was used to refine the distribution and mechanical properties of the dampers. Thorough assessments of the refined design were carried out following several design guidelines, including ASCE 41, FEMA 351, and FEMA P‐58. The results indicated that the proposed retrofit method of using fluid viscous dampers could achieve the retrofit goal and provide a cost‐effective means of improving the structural behavior and reducing economic losses in a major seismic event.     

Seismic design of special moment‐resisting steel frame with prevention of soft‐storey mechanism failure

Most structures with masonry infills that are continuous along their height, which are interrupted in the lowest storey, are damaged by earthquakes. These structures are anticipated to collapse due to the undesirable soft‐storey mechanism formed by lateral stiffness of masonry infills in other storeys. The seismic design criteria of UBC97 code for special moment‐resisting steel frame (SMRSF) are reviewed. In this paper, a new criterion for seismic design of such structures is presented. The proposed criteria are used to design three SMRSFs: 5, 8 and 15 storeys. Nonlinear time‐history dynamic analyses are applied for the designed SMRSFs based on the proposed criteria. Displacements and storey drifts, which are obtained by the proposed method, are compared with nonlinear time‐history dynamic analysis results, finally. Copyright © 2011 John Wiley & Sons, Ltd.